2005/04/20 by Suresh K Maran, Maran, Suresh K
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0504092
Title has been changed. Many important changes has been made from the previous version. The systematic derivation of the spin foam models of SO(4,C) general relativity has been explained using picture equations. The details of the reality constraints has been modified. Additional sections has been introduced. One of them deals with the asymptotic limit of the spin foams with new results. English has been improved, sections edited and reorganized
openalex publication_date 2005/04/20 · arxiv created 2005/09/25 · arxiv updated 2016/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Barrett-Crane model for the SO(4,C) general relativity is systematically derived. This procedure makes rigorous the calculation of the Barrett-Crane intertwiners from the Barrett-Crane constraints of both real and complex Riemannian general relativity. The reality of the scalar products of the complex bivectors associated with the triangles of a flat four simplex is equivalent to the reality of the associated flat geometry. Spin foam models in 4D for the real and complex orthogonal gauge groups are discussed in a unified manner from the point of view of the bivector scalar product reality constraints. Many relevant issues are discussed and generalizations of the ideas are introduced. The asymptotic limit of the SO(4,C) general relativity is discussed. The asymptotic limit is controlled by the SO(4,C) Regge calculus which unifies the Regge calculus theories for all the real general relativity cases. The spin network functionals for the 3+1 formulation of the spin foams are discussed. The field theory over group formulation for the Barrett-Crane models is discussed briefly. I introduce the idea of a mixed Lorentzian Barrett-Crane model which mixes the intertwiners for the Lorentzian Barrett-Crane models. A mixed propagator is calculated. I also introduce a multi-signature spin foam model for real general relativity which is made by splicing together the four simplex amplitudes for the various signatures. Further research that is to be done is listed and discussed.